We have obtained deep images in the near-infrared J and K filters for several fields in the Local Group galaxy WLM .
We report intensity mean magnitudes for 31 Cepheids located in these fields which we previously discovered in a wide-field optical imaging survey of WLM .
The data define tight period-luminosity relations in both near-infrared bands which we use to derive the total reddening of the Cepheids in WLM and the true distance modulus of the galaxy from a multiwavelength analysis of the reddened distance moduli in the VIJK bands .
From this , we obtain the values E ( B-V ) = 0.082 \pm 0.02 , and ( m - M ) _ { 0 } = 24.924 \pm 0.042 mag , with a systematic uncertainty in the distance of about \pm 3 % .
This Cepheid distance agrees extremely well with the distance of WLM determined from the I-band TRGB method by ourselves and others .
Most of the reddening of the Cepheids in WLM ( 0.06 mag ) is produced inside the galaxy , demonstrating again the need for an accurate determination of the total reddening and/or the use of infrared photometry to derive Cepheid distances which are accurate to 3 % or better , even for small irregular galaxies like WLM .